Find the area of triangleABC with B=47.6degrees, a=3.6, and c= 9.7. Round your answer to the nearest tenth.
To find the area of triangle ABC, we can use the formula:
Area = 0.5 * a * c * sin(B)
Given that B = 47.6 degrees, a = 3.6, and c = 9.7, we can substitute these values into the formula:
Area = 0.5 * 3.6 * 9.7 * sin(47.6)
First, we need to convert the angle B from degrees to radians because the sine function in most mathematical functions expects angles in radians. To convert from degrees to radians, we multiply the value by π/180.
B_radians = 47.6 * π/180
Next, we can use a calculator to find the value of sin(B_radians).
sin(B_radians) ≈ 0.7317
Now, we can substitute this value back into the formula:
Area = 0.5 * 3.6 * 9.7 * 0.7317
Using a calculator to evaluate this expression, we find:
Area ≈ 12.6149
Rounding this value to the nearest tenth, we get:
Area ≈ 12.6
So, the area of triangle ABC, rounded to the nearest tenth, is approximately 12.6 square units.